YB  10887 


SWITCH  LAYOUTS 
CURVE"  EASEMENTS 


REESE  LIBRARY 


L,_n— n— n__n — n — n, 


£      \    UNIVERSITY  OF  CALIFORNIA 


v4cce&sion  No.y 5~Q  H  */  •   C/.mNo. 


SWITCH    LAYOUTS 

SHOWING  GRAPHICALLY  THE  LEADS,  OFFSETS  AND  ALL  DIMENSIONS  NEEDED  FOR  LOCATING 
FROGS  OF  ALL  NUMBERS  AND  CURVES  IN  ALL  SWITCHES  IN  COMMON  USE. 


CURVE    EASEMENTS 

TABLES  OF  ANGLES,  CHORDS  AND  DEFLECTIONS  FOR  EASING  THE  TRANSITION  FROM  A  TANGENT 

TO  A  CURVE,  AND  FROM  A  CURVE  OF  ONE  RADIUS  TO  A  CURVE  OF  ANOTHER  RADIUS. 


BY 


AUOUSTUS    TORRKY, 

PRINCIPAL  ASSISTANT  ENGINEER,  MICHIGAN  CENTRAL  RAILROAD. 


COPYRIGHT,  1892, 

BY 
THE  RAILROAD  GAZETTE. 


CONTENTS. 

SWITCH  LAYOUTS.  PAGE. 

Explanation  of  Diagrams  for  Laying  Out  Switches  and  Crossovers      ....  5-12 

Table  of  Frogs  and  Leads IB 

Single  Split-Switches 14-22 

Double  Split-Switches 23-95 

Single  Stub-Switches 96-104 

Double  Stub-Switches  .        .        .        .       (.   ' 105-122- 

Locations  of  Frogs  in  Crossovers .        .        .         .123 

Middle  Ordinates  for  Bending  Rails 124-125 

CURVE  EASEMENTS. 

Explanation  of  Plates,  Cases  and  Tables                        , 127-142 

Plates  I.  to  VII.:    Functions  of  Transition  Curves 143-149 

Cases  I.  to  IV. :    Calculations  for  Tangent  Lengths,  Radii  and  Easements        .         .  150-155 
Tables  I.  to  X. :    Functions  of  Transition  Curves  for  Chords  100  ft.  to  25  ft.,  and  1°  to 

15'  Variation .  156-191 

Tables  XL  to  XVIII.:    Simple  Curves,  1°  to  7°  30' 184-191 


LAYING  OUT  SWITCHES  AND  CROSSOVERS, 


The  theoretical  point  of  a  frog  may  be  found  as  follows  :  Mark  the 
place  where  the  frog  is  4  inches  wide  from  gauge  to  gauge;  from  this  as  a 
beginning,  measure  toward  the  point  4  times  as  many  inches  as  the  num- 
ber of  the  frog.  Mark  the  wing  rail  opposite,  and  the  latter  mark  will  be 
opposite  the  theoretical  point  of  frog. 

The  figures  given  in  the  diagrams  for  the  leads  (distance  from  the  point 
of  the  frog  to  the  head-block)  to  frogs  in  straight  main  track  apply  to  frogs 
in  the  curved  main  track,  provided  the  main  track  forms  a  simple  curve 
within  the  limits  of  the  lead,  except  as  to  the  degree  of  curve  of  the  lead. 

When  the  frog  is  in  the  outside  rail  of  the  curve  of  the  main  track,  the 
degree  of  curve  of  the  lead  will  equal  the  degree  of  curve  of  the  main 


6  SWITCHES    AND    CROSSOVERS. 

track  minus  the  degree  of  curve  of  the  lead  given  in  the  diagram.  When 
the  frog  is  in  the  inside  rail  of  the  carve  of  the  main  track,  the  degree  of 
curve  of  the  lead  will  equal  the  degree  of  curve  of  the  main  track  plus 
the  degree  of  curve  of  the  lead  given  in  the  diagram. 

In  calculating  the  lengths  and  curves  of  leads  the  stiffness  of  frogs 
near  the  points  has  been  considered,  and  for  this  reason  it  has  been  as- 
sumed that  the  legs  of  frogs  cannot  be  bent  nearer  to  the  point  than  3  ft. 
The  recognition  of  this  fact  is  of  especial  importance  in  the  case  of  a  nest  of 
frogs  coupled  so  closely  together  as  they  are  in  some  of  the  combinations 
shown  in  the  diagrams. 

Lead  rails  and  the  unbolted  part  of  the  legs  of  frogs  should  be  bent  to 
the  proper  curve  before  being  spiked  down,  and  for  this  purpose  a  table 
for  bending  rails  of  any  length  to  any  degree  of  curve  is  given. 

The  offsets  shown  at  different  points  on  the  drawings  of  the  layouts 
are  measured  from  the  gauge  side  of  the  rails.  These  offsets  are  exactly 
true  only  when  the  angle  of  a  frog  accords  with  its  reputed  number  and 
when  the  lead  is  put  in  precisely  as  the  figures  given  in  its  diagram  require. 


SWITCHES    AND    CROSSOVERS.  7 

In  using  tlie  figures  from  the  diagrams,  always  begin  at  the  frog  end  of 

the  lead  and  measure  the  partial  distances  from  the  theoretical  point  of 

frog  toward  the  head  block.     If  made  strictly  at  the  points  indicated  by 

these  partial  distances,  the  offsets  given  on  the  drawings  will  result  in  a 

lead  which  is  exactly  right,  if  the  angle  of  the  frog  is  exactly  right,  and 

nearly  right  if  the  angle  of  the  frog  is  nearly  right.     The  use  of  the  offset 

\   enables  a  man  with  an  unpracticed  eye  to  lay  a  perfectly  correct  lead  and 

|   also  avoids  the  necessity  for  lining  the  rails  before  spiking  them. 

Ties  should  be  laid  in  the  same  order  as  listed  under  each  diagram, 
1   and  with  20-in.   centres,  unless  such  spacing  interferes  with  switch  con- 
nections or  the  proper  spiking  of  the  joints.      If  the  standard  length  of 
the  tie  on  any  road  is  longer  or  shorter  than  y  ft.,  the  difference  must  be 
added  to  or  taken  from  the  lengths  of  the  ties  as  given. 

The  figures  given  for  split  switches  apply  exactly  only  to  points  15 
ft.  long  with  a  5f-in.  offset  from  the  stock-rail  at  the  heel  of  the  point. 
The  planing  of  15-ft.  points  varies,  however,  so  slightly,  in  so  far  as  it 
affects  the  angle  made  with  the  stock-rail,  that  the  figures  given  for 


8  SWITCHES    AND    CROSSOVERS. 

lengths  of  lead  and  intermediate  offsets  will  be  applicable  to  most  of  the 
15-ft.  points  in  use. 

In  split  switches  the  point-rail  is  that  part  of  the  lead  which  turns 
the  truck  most  abruptly.  For  that  reason  it  has  not  been  thought  advis- 
able to  consider  a  point-rail  which  makes  a  sharper  angle  than  the  one 
shown  in  this  work.  Fifteen  feet  is  an  economical  length  at  which  to  cut 
points,  and  5 £  in.  allows  room  for  a  spike  at  the  heel  of  the  point  rail 
when  its  base  does  not  exceed  5  in.  It  does  not  ease  the  transition  from 
the  main  track  to  the  curve  of  the  lead,  nor  does  it  lessen  the  curvature 
of  the  lead  appreciably,  to  curve  the  point-rails  on  their  unplaned  portion. 
In  consequence  the  point-rail  has  been  considered  straight  throughout  its 
whole  length  in  these  calculations.  With  the  point-rails  turned  for  the 
side  track,  it  is  probable  that  the  heel  of  the  planed  portion  will  not 
always  touch  the  stock  rail  if  the  joint  at  the  heel  of  the  point-rail  is 
fully  bolted,  but  the  passage  of  a  track  will  have  the  effect  of  forcing  it 
there,  making  the  point-rail  tangent  to  the  curve  of  the  lead,  although  its 
appearance  may  not  indicate  it  when  the  switch  is  not  in  use. 


SWITCHES    AND    CROSSOVERS.  9 

In  the  diagrams  of  combinations  consisting  of  two  split  switches  and 
three  frogs,  that  diagram  is  first  given  which  provides  not  less  than  2  in. 
clear  room  for  attaching  rod  No.  1  to  the  second  switch  point,  when  the 
rail  has  a  base,  and  the  switch-stand  a  throw,  of  not  to  exceed  5  in.  In 
the  case  of  a  narrower  rail-base,  or  less  throw  to  the  switch-stand,  the  clear- 
ance is  of  course  greater,  but  2  in.  will  admit  of  a  special  head-rod  connec- 
tion without  interfering  with  the  point-rail  of  the  first  switch.  On  the  suc- 
ceeding page  will  be  found  a  diagram  of  a  combination  of  frogs  which 
takes  up  less  room  in  the  track,  but  which  requires  that  the  flange  of  the 
lead-rail  of  the  first  switch  shall  be  cut  away  to  allow  room  for  the  pas- 
sage of  the  head-rod  of  the  second  switch.  From  an  inspection  of  these 
combinations,  which  are  designed  in  such  a  way  as  to  provide  for  the  use 
of  ordinary  frog  angles,  it  will  be  seen  that  many  of  them  are  undesirable 
for  general  use  on  account  of  the  close  or  special  work  necessary  for  coup- 
ling the  frogs  together  and  for  arranging  the  wing-rails. 

In  cases  where  both  switches  turn  toward  the  same  side  of  the  main 
track,  it  is  evident  that  one  of  the  tracks  shown  in  the  diagrams  as  a,  turn- 


10  SWITCHES    AND    CROSSOVERS. 

out  from  the  main  track  becomes  the  main  track,  and  the  degree  of  curva- 
ture of  the  first  lead  equals  the  sum  of  the  degrees  of  curvature  of  both 
leads  in  the  table.  The  other  dimensions,  although  not  mathematically 
exact  for  this  change,  are  practically  so  if  the  main  track  is  a  straight  line 
or  a  simple  curve.  It  is  important  to  notice  in  the  diagram  which  frog 
is  ahead,  although  it  does  not  matter  on  which  side  of  the  track  it  is. 

The  leads  of  stub  switches  are  computed  on  the  same  premises  with 
regard  to  frogs  as  are  the  leads  of  split  switches.  The  moving  rail  is  in  no 
case  regarded  as  moving  more  than  22  ft.  back  from  the  head-block,  and 
has  a  switch  stand  throw  of  5  in.  If  more  rail  than  22  ft.  is  left  unspiked 
it  is  unlikely  that  it  will  be  affected  by  the  movement  of  the  switch-stand. 
While  it  is  probable  that  the  moving  rail  will  in  practice  assume  a  curve 
differing  somewhat  from  a  circular  curve,  it  has  been  regarded  as  a 
simple  curve  in  these  calculations,  either  of  the  same  degree  as  the  rest  of 
the  lead,  or  of  that  degree  due  to  a  deflection  of  5  in.  from  a  straight  line 
in  22  ft. 

The  same  general  facts  alluded  to  above  which  apply  to  combinations 


SWITCHES    AND    CROSSOVERS.  11 

of  split  switches  are  true  of  3-throw  stub  switches,  which  latter,  however, 
are  for  many  economic  reasons  to  be  avoided  if  possible.  The  lengths  of 
leads  given  in  the  diagrams  differ  a  little  from  some  in  use,  mainly  because 
the  rigidity  of  the  frog  is  regarded  as  a  necessary  factor  in  these  calcula- 
tions. If  the  leads  of  the  switches  given  are  shortened  the  degree  of  cur- 
vature is  evidently  increased,  while  if  the  leads  are  lengthened,  a  portion 
is  just  as  positively,  though  perhaps  less  evidently,  increased  in  degree  of 
curvature.  The  simple  curve  which  unites  the  tangent  at  the  frog  with 
the  tangent  of  the  switch-rail  at  the  switch-stand  is  therefore  the  easiest 
and  the  best  line  to  follow. 

The  diagrams  showing  the  positions  of  frogs  in  crossovers  give  the 
proper  location  of  the  frogs  when  the  main  tracks  are  straight  and  con- 
nected by  a  piece  of  straight  track,  or  when  the  main  tracks  are  curved, 
and  the  frogs  are  connected  by  a  piece  of  track  whose  degree  and  direc- 
tion of  curvature  is  the  same  as  that  of  the  main  tracks. 

Owing  to  the  condition,  in  the  leads  of  frogs  of  small  angles,  that  the 
point  rail  makes  a  much  greater  deflection  from  the  stock  rail  than  15  ft. 


12  SWITCHES    AND    CROSSOVERS. 

of  the  lead  curve  would  make,  it  follows  that  the  lead  from  point  of  switch 
to  frog  is  virtually  a  compound  curve  with  its  sharper  portion  at  the  point 
end.  This  compound  curve  of  lead  sometimes  becomes  a  reversed  curve 
when  a  frog  is  in  the  outside  rail  of  a  curve  sharper  than  the  lead  of  a  sim- 
ilar frog  in  straight  track,  and  the  lead  will  look  awkward  when  the 
above  limit  of  curvature  of  main  track  is  approached.  A  remedy  for  thi , 
awkward  appearance,  which  can  be  applied  in  many  cases,  is  to  reduce  the 
bend  in  the  stock  rail  and  put  the  balance  of  the  bend  in  the  opposite  rail 
of  main  track,  which  is  ordinarily  kept  straight.  This  introduces  a  com- 
pound curve  in  the  main  track  between  the  frog  and  the  beud,  and  the 
offsets  to  lead  given  in  the  table  will  not  apply  exactly,  but  the  standard 
length  of  lead  will  be  nearly  enough  correct.  It  follows  from  the  foregoing 
that  a  wide  frog  generally  looks  better  on  the  outside  of  a  curve,  and  that  it 
is  advisable  in  a  combination  of  frogs  to  put  the  wider  one  in  the  outside 
rail  of  a  curved  main  track. 


TABLE  OF  FROGS  AND  LEADS.  13 

GAUGE  4  FT.  8^  IN.  (4.71  FT  ).    MEASUREMENTS  IN  FEET  AND  TENTHS  OF  A  FOOT. 


^No.  of 
frog. 

Frog 
angle. 

SPLIT  SWITCH. 

STUB  SWITCH. 

No.  of 
frog. 

4 

Lead  H.B. 
to  Frog. 

Fly 
rail. 

Deg.  of 
curve. 

Total  dist. 
on  rail. 

Switch 
rail. 

Lead  H.B. 
to  Frog. 

Deg.  of 
curve. 

4 

14°  j&5' 

42.28 

15.0 

52°  51' 

34.67 

10.40 

24.27 

45°  36' 

•5 

11°  25' 

49.23 

15.0 

30°  44' 

44.12 

13.21 

30.91 

27°  49' 

5 

« 

9°  32' 

55.47 

15.0 

20°  31' 

53.45 

16.00 

37.45 

19°  09' 

6 

7 

8°  10' 

61.45 

15.0 

14°  33' 

62.98 

18.83 

44.15 

13°  36' 

7 

8 

7°    9' 

67.12 

15.0 

10°  48' 

72.45 

21.65 

50.80 

10°  17' 

8 

9 

6°  22' 

72.43 

15.0 

8°  18' 

77.92 

22.00 

55.92 

7°  55' 

9 

10 

5°  44' 

77.41 

15.0 

6°  33' 

82.64 

22.00 

60.64 

6°    8' 

10 

11 

5°  12' 

80.00 

15.0 

5°  54' 

87.00 

22.00 

65.00 

4°  54' 

11 

12 

4°  48' 

87.01 

15.0 

4°  15' 

91.52 

22.00 

69.52 

3°  52' 

13 

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CURVE  EASEMENTS. 


Transitions  from  tangent  to  curve  or  from  lighter  curve  to  sharper 
curve  by  the  introduction  of  equal  chords  of  regularly  increasing  degree 
of  curvature. 

The  object  of  easing  curves  at  their  extremities  is  to  turn  the  truck 
gradually,  and  thus  avoid  shock  to  car  and  rail,  and  also  to  secure  a  grad- 
ually increasing  elevation  of  the  outer  rail,  without  having  that  elevation  un- 
duly great  at  any  point.  It  is  manifest  that  the  elevation  due  to  a  sharp 
curve  cannot  be  used  at  the  point  where  that  curve  is  changed  to  a  straight 
line  without  carrying  a  decreasing  elevation  for  some  distance  from  the 
point  of  curve  along  the  straight  line.  This  elevation  on  the  straight  line, 


128  CURVE   EASEMENTS. 

if  at  all  pronounced,  gives  an  unpleasant  sensation,  and  it  is  the  aim  of 
good  trackmen  to  adapt  the  line  at  the  ends  of  curves  to  the  super-eleva- 
tion which  they  have  to  reach.  The  practical  result  of  lining  this  part  of 
the  track  by  eye  generally  introduces  an  unnecessarily  fiat  piece  of  curve 
and  an  unnecessarily  sharp  piece  of  curve  into  the  transition,  and  the 
changing  super-elevation  seldom  accords  throughout  the  transition  with 
the  changing  degree  of  curve. 

The  method  pursued  in  the  following  tables  secures  a  practically 
gradual  transition,  the  ease  of  passage  being  dependent  upon  the  length 
of  chords  used  and  upon  the  amount  of  change  in  the  degree  of  curvature 
of  successive  chords.  The  stakes  for  lining  the  transitions  can  scarcely 
be  set  except  by  an  engineer.  The  formulas  for  the  various  cases  are 
within  the  easy  comprehension  and  use  of  a  competent  surveyor.  The 
functions  of  the  transition  curve  which  are  used  in  the  formulas  and  in 
laying  out  the  work  are  illustrated  by  the  seven  "plates"  immediately  suc- 
ceeding this  text. 

In  the  "tables"  (I.  to  X.  inclusive)  the  equal  chords  AB,  BC,  CD,  and 


CURVE   EASEMENTS. 

DE,  of  the  transition  curves  (AE  of  plates)  are  designated  by  the  degree 
of  the  curve  they  subtend. 

That  end  of  an  equal  chord  which  joins  an  equal  chord  o(  less  cur* 
vature  is  designated  as  the  "  small  end,"  the  other  as  the  <fr large  end;'? 
thus  B  is  the  "  small  end"  and  C  is  "  large  end"  of  chord  BC,  of 
plates. 

The  transition  curve  uniting  a  tangent  with  a  central  curve  of  given 
degree  of  curvature  should  begin  with  its  chord  of  least  degree  of  curva- 
ture and  be  carried  to  the  u  large  end"  of  the  chord  whose  degree  of  cur- 
vature is  next  below  that  of  the  central  curve.  For  example,  to  unite  a 
8°  curve  with  a  tangent,  the  suitable  transition  curve  by  Table  IV.  is  the 
chords  0°  30'  to  2°  30'  inclusive.  By  Table  X.  the  suitable  transition  curve 
is  the  chords  0°  15'  to  2°  45'  inclusive. 

The  transition  curve  uniting  branches  of  a  com  pound  curve  should  be 
bet  ween  the  limits  of  the  chord  whose  degree  of  curvature  is  next  above 
that  of  the  lighter  one  of  the  branches  of  the  compound  curve,  and  the 
chord  whose  degree  of  curvature  is  next  below  that  of  the  sharper  one  of 


130  CURVE    EASEMENTS. 

the  branches  of  the  compound  curve .  For  example,  to  unite  a  6°  curve  with 
a  2°  curve,  a  suitable  transition  curve,  by  Table  III.,  is  the  chords  3°  to  5° 
inclusive.  By  Table  IX.  the  suitable  transition  curve  is  the  chords  2°  30' 
to  5°  30'  inclusive.  The  limitations  of  the  transition  curve  having  been 
determined  as  above,  the  functions  used  in  formulas  (under  "cases"  1  to  4 
inclusive)  are  taken  from  Sections  A,  B,  C,  D  and  E  of  such  one  of  the 
Tables  I.  to  X.  inclusive,  as  represents  the  transition  adopted  as  suitable* 
Sections  UB"  of  the  tables  give,  above  the  heavy  horizontal  lines  of 
tables,  offsets  from  the  tangent  through  the  "  small  end"  of  the  chord 
marked  at  head  of  column  to  the  "large  end"  of  the  chords  marked  on 
the  right.  For  example,  in  the  transition  represented  by  Table  IV.,  the 
offset  from  the  tangent  through  the  '  small  end"  of  the  0°30'  chord  to  the 
" large  end"  of  the  2°  30'  chord  is  found  above  the  heavy  horizontal  line 
of  Table  IV.,  Section  "B,"in  column  marked  at  the  head  of  0°  30' and 
in  space  marked  on  the  right  2°  3u;,  and  it  is  6.00  ft.  Also,  for  further 
example,  in  the  transition  represented  by  Table  JX?.,  the  offset  from  the 
tangent  through  the  "  small  end "  of  the  2° 30'  chord  to  the  "large  end " 


CUEVE   EASEMENTS.  131 

of  the  5°  30'  chord  is  found  above  heavy  horizontal  line  of  Table  IX.,  Sec- 
tion "B,"  in  column  marked  at  the  head  2°  30'  and  in  space  marked  on 
the  right  5°  30',  and  it  is  9.15  ft.  These  "  offsets"  are  illustrated  by 
Plate  1. 

Sections  "B"  of  the  tables  give  below  the  heavy  horizontal  lines 
of  tables  the  projections  upon  the  tangent  through  the  " small  end"  of 
chord  marked  at  foot  of  column,  of  the  lines  joining  that  point  of  tangent 
with  the  " large  end"  of  the  chords  marked  on  the  left.  These  lines  join- 
ing the  ends  of  the  equal  chords  are  hereafter  designated  "  long  chords." 
For  example,  in  the  transition  represented  by  Table  IV.,  the  projection 
upon  the  tangent  through  the  "small  end"  of  the  0°30'  chord  of  the 
"long  chord"  joining  the  "small  end"  of  the  0°  30' chord  with  the  "large 
end"  of  the  2°  30'  chord,  is  found  below  heavy  horizontal  line  of  Table 
IV.,  Section  "B,"  in  column  marked  at  the  foot  0°  30' and  in  space 
marked  on  the  left  2°  30',  and  it  is  249.88  ft.  Also,  for  further  example, 
in  the  transition  represented  by  Table  IX.,  the  projection  upon  the  tan- 
gent through  the  "  small  end"  of  the  2°  30'  chord,  of  the  "long  chord/' 


132  CURVE   EASEMENTS. 

joining  the  "small  end"  of  the  2°  30'  chord  with  the  "large  end"  of  the 
5°  30'  chord,  is  found  below  heavy  horizontal  line  of  Table  IX.,  Section 
"  B.,"  in  column  marked  at  the  foot  2°  30' and  in  space  marked  on  the  left 
5°  .3u,  and  it  is  174. 65  ft. 

These  "projections  of  long  chords  upon  tangents  "  are  illustrated  by 
Plate  2. 

{Sections  u  C  "  of  the  tables  give  the  prolongations  of  the  radii  to  tan- 
gent through  the  "small  end"  of  chord  at  head  of  first  column  from  the 
"large  end"  of  the  chord  in  that  and  other  columns.  For  example,  in 
the  transition  represented  by  Table  IV^.,  the  prolongation  of  the  radius 
through  the  "large end"  of  the  2°  30'  chord  to  the  tangent  through  the 
"small  end"  of  the  0°  30'  chord  is  found  in  Table  IV.,  Section  "C",  in 
column  marked  2°  bO',  and  it  is  6.01  ft. 

Also,  for  further  example,  in  the  transition  represented  by  Table  X., 
the  prolongation  of  the  radius  through  the  "large  end"  of  the  2°  45' 
chord  to  the  tangent  through  the  "small  end"  of  the  0°  15'  chord  is 
found  in  Table  X.,  Section  "C",  in  column  marked  2°  -15',  and  it  is 


CURVE   EASEMENTS.  133 

6.91ft  These  "prolongations  of  radii  to  tangent"  are  illustrated  by 
Plate  3. 

Sections  "  D"of  the  tables  give  above  the  heavy  horizontal  lines  of 
tables,  the  lengths  of  the  "long  chord"  joining  the  "small  end"  of  the 
chords  marked  at  head  of  column,  with  the  "large  end"  of  the  chords 
marked  on  the  right.  For  example,  in  the  transition  represented  by  Table 
IV.,  the  length  of  the  "long  chord"  joining  the  "small  end"  of  the 
0°  30'  chord  with  the  "large  end"  of  the  2°  30'  chord  is  found  above  heavy 
horizontal  line  of  Table  IV.,  Section  "D",  in  column  marked  at  the  head 
0°  30',  and  in  the  space  marked  on  the  right  2°  3u',  and  it  is  249.96  ft. 

Also,  for  further  example,  in  the  transition  represented  by  Table  IX., 
the  "long  chord"  joining  the  "small  end"  of  the  2°  30'  chord  with  the 
"large  end"  of  the  5°  30'  chord  is  found  above  heavy  horizontal  line  of 
Table  IX.,  Section  "D,"  in  column  marked  at  the  head  2°  30'  and  in 
space  marked  on  the  right  5°  30',  and  it  is  174.89  ft.  These  "long  chords" 
are  illustrated  by  Plate  4. 

Sections  "D"  of  the  tables  give  below  the  heavy  horizontal  lines  of 


134  CURVE    EASEMENTS. 

tables  the  angles  between  the  tangent  through  the  u small  end"  of  the 
chord  marked  at  foot  of  column,  and  the  tangent  through  the  "large 
end"  of  chord  markel  at  left.  The  angles,  therefore,  represent  the 
amount  of  change  in  direction  accomplished  within  the  limits  of  the  tran- 
sition. For  example,  in  the  transition  represented  by  Table  lVr.,  the  angle 
between  the  tangent  through  the  "  <mall  end"  of  the  0°  W  chord  and  the 
tangent  through  the  u large  end"  of  the  2°  30'  chord  is  found  below  the 
heavy  horizontal  line  of  Table  IV.,  Section  UD,"  in  column  marked  at 
the  foot  0°  3v/  and  in  space  marked  on  the  left  2°  3o',  and  it  is  3°  45'. 
For  further  example,  in  the  transition  represented  by  Table  IX.  the  angle 
between  the  tangent  through  the  usmall  end"  of  the  2°  3u'  chord  and  toe 
tangent  through  the  "large  end"  ol  the  5°  3o'  chord  is  found  below  the 
heavy  horizontal  line  of  Table  IX  ,  Section  "D,"  in  column  marked  at 
the  foot  2°  3u'  and  in  space  marked  on  the  left  6°  30',  and  it  is  7°.  The 
"curvature  due  to  compounding"  is  illustrated  by  Plate  5. 

Sections  "E"  of  the  tables  give  the  distances  on  the  tangent  through 
the  "  small  end"  of  the  chord  marked  at  head  of  h'rst  column,  from  that 


CURVE   EASEMENTS.  135 

point  of  tangent  to  an  intersection  with  radii  prolonged  through  the  "  large 
ends"  of  that  chord  and  the  chords  marked  at  the  head  of  other  columns. 
For  example,  in  the  transition  represented  by  Table  IV.,  the  distance  on 
the  tangent  through  the  "  small  end"  of  the  0°  3u'  chord  from  the  tangent 
point  to  the  intersection  with  the  radius  prolonged  through  the  u  large 
end"  of  the  2°  8u'  chord,  is  found  in  Table  IV.,  Section  "  E"  in  column 
marked  2°  80',  and  it  is  250.28  ft. 

For  further  example,  in  the  transition  represented  by  Table  X.,  the 
distance  on  the  tangent  through  the  u  small  end"  of  the  u°  15'  chord,  from 
the  tangent  point  to  ths  intersection  with  the  radius  prolonged  through  the 
u  large  end"  of  the  v°  45'  chord,  is  fouud  in  Table  X.,  Section  "E,"  in 
column  marked  2°  45',  and  it  is  275.85  ft.  This  "  tangent  length  of  com- 
pounding' '  is  illustrated  on  Plate  8  The  limits  of  the  curve  wit  a  its  tran- 
sition having  been  determined  by  formulas  in  cases  1  to  4  inclusive,  the 
points  of  transition  may  be  established  by  the  deflection  angles  found  in 
Sections  "  A"  of  the  tables. 

The  angles  below  the  heavy  horizontal  lines  of  tables  are  those  between 


136  C\JP,VE    EASEMENTS. 

the  tangent  through  the  "  small  end"  of  the  chord  marked  at  bottom  of 
column  and  lines  from  that  point  of  tangent  to  the  ''large  ends"  of  the 
chords  marked  on  the  left.  These  angles  are  illustrated  on  Plate  6.  The 
angles  above  the  heavy  horizontal  lines  of  tables  are  those  between  the 
tangent  through  the  u  large  end  "  of  the  chord  marked  at  head  of  column 
and  lines  from  that  point  of  tangent  to  the  " small  end"  of  the  chords 
marked  on  the  right.  These  angles  are  illustrated  on  Plate  7.  For 
example,  it  is  desired  to  set  stakes  for  transition  from  a  tangent  up  to  a  3° 
curve,  using  chords  of  5o  ft.  length,  varying  15'  in  degree  of  curvature. 
The  angles  to  turn  off  are  found  in  Table  V.,  Section  i4  A  ".  The  point  of 
curve  is  in  this  case  the  "small  end"  of  the 0°  15'  chord,  and  the  angles  to 
turn  from  a  set  up  at  this  point  are  found  below  the  heavy  horizontal  line 
of  Table  V.,  Section  "A,"  in  column  marked  0°  15'  at  its  foot.  The  deflec- 
tion to  the  "large  end  "  of  the  0°  15'  chord  is  3J-',  and  is  found  in  this  column 
in  the  space  marked  0°  15'  on  left.  The  deflection  from  same  set  up  to  the 
"large  end  "  of  the  0°  3u'  chord  is  9£',  and  so  on  to  a  deflection  of  2°  52£'  to 
the  "large  end"  of  the  2°  45'  chord. 


CURVE   EASEMENTS.      .  137 

The  angle  between  the  "long  chord"  joining  the  "large  end"  of  the 
2°  45'  chord  with  the  " small  end"  of  the  0°  lo'  chord,  and  the  tangent  at 
the  "  large  end"  of  the  2°  45'  chord,  is  found  above  the  heavy  horizontal 
line  of  table  in  column  marked  2°  45'  at  the  head,  and  in  the  space  marked 
0°  15'  on  the  right,  and  it  is  5°  22J-'. 

It  may  be  necessary  to  make  an  intermediate  set  up  as  at  the  "  large 
end"  of  the  1°  15'  chord.  The  deflection  to  this  point  from  the  tangent 
through  the  u small  end"  of  the  0°  1ft'  chord  is 41'.  The  angle  which  the 
"long  chord"  connecting  the  " large  end"  of  the  1°  15'  chord  with  the 
"small  end"  of  the  0°  15'  chord  makes  with  the  tangent  through  the 
"large  end  "  of  the  1°  15'  chord  is  found  above  the  heavy  horizontal  line 
of  table  in  column  marked  at  the  head  1°  16',  and  in  space  marked  on  right 
0°  15',  and  it  is  1°  ll£'.  From  this  tangent,  which  is  the  tangent  through 
the  "large  end"  of  the  1°  15'  chord,  or  through  the  "small  end"  of  the 
1°  3</  chord,  the  deflections  to  continue  the  curve  are  found  below  the 
heavy  horizontal  line  of  table  in  column  marked  at  the  foot  1°  30',  and 
they  are  2^',  47',  1°  43',  2°  15'  and  2°  49J'. 


138  ,       CUBVE   EASEMENTS. 

The  angle  at  the  " large  end"  of  the  2°  46'  chord  or  at  the  beginning 
of  the  3°  chord,  between  the  "long  chord"  joining  the  "large  end"  of 
the  2°  45'  chord  \*ith  the  "  small  end  "  of  the  1°  so'  chord  and  the  tangent 
through  the  "large  end"  of  the  2°  46'  chord,  is  found  above  the  heavy- 
horizontal  line  of  table  in  column  marked  at  the  head  2°  4.5'  and  in  space 
marked  on  the  right  1°  30',  and  is  3°  33'. 

In  locating  points  for  the  same  transition  from  the  end  of  the  3° 
chord  to  the  tangent,  the  first  set  up  is  at  the  "large  end"  of  the  2°  45' 
chord,  and  the  deflections  are  turned  from  the  tangent  through  that  point 
to  the  "small  end"  of  the  successive  chords.  The  deflections  are  found 
above  the  heavy  horizontal  lines  of  table  in  columns  marked  2°  45'  at  the 
head  and  are  to  "small  ends "  of  the  chords  marked  on  the  right.  They 
are  41 J',  1°  20%',  etc.,  to  .F>°  22|',  which  last  deflection  is  to  the  "small  end" 
of  the  0°  15'  chord,  or  the  end  of  the  transition.  The  angle  between  the 
"  long  chord  "  joining  the  "small  end  "  of  the  o°  15'  chord  with  the  "large 
end"  of  the  2°  45'  chord,  and  the  tangent  through  the  "  small  end"  of  the 
0°  15'  chord,  is  found  below  the  heavy  horizontal  line  of  table  in  column 


CURVE   EASEMENTS.  139 

marked  at  the  foot  0°  15'  and  in  space  marked  on  the  left  2°  45',  and  it  is 
2°  52£'.  If  an  inrermediate  set  up  is  used  the  angles  are  found  in  a  similar 
way  to  that  already  described. 

Case  I.  illustrates  the  ordinary  joining  of  two  tangents  of  location  with 
any  desired  curve  eased  by  a  similar  transition  carve  at  each  end,  and  ap- 
plies where  the  exact  point  of  curve  and  point  of  tangent  are  not  of  such 
material  consequence  as  other  features  of  location  are. 

In  making  a  "  paper  location/'  it  may  be  necessary  to  show  just  where 
the  central  part  of  an  ea  ed  curve  will  lie.  This  position  can  be  shown 
correctly  between  the  limits  of  the  "  central  curve"  by  uniting  parallel 
tangents  with  a  simple  curve  of  the  same  degree  of  curvature  as  the 
"  central  curve/' 

These  parallel  tangents  will  lie  inside  the  tangents  of  location,  an 
amount  equal  to  the  <k  offset  from  tangent  to  end  of  chord,"  at  junction  of 
easement  and  "central  curve"  (see  QE.3  Plate  L),  less  the  product  of  the 
sine  of  J  the  "  curvature  due  to  compounding"  ^FOof  ftfleJL^  by  that 


140  CURVE   EASEMENTS. 

length  of  the  u  central  curve"  which  would  be  required  to  accomplish  the 
curvature  represented  by  KFC.  For  instance,  to  determine  where 
a  4°  curve  eased  by  transition  given  in  Table  IV.  would  lie.  In  this 
case  QE  =  15.26  ft.  and  KFC  =  7°.  The  amount  of  4°  curve  required 
to  accomplish  1°  of  curvature  is  175  ft.  Therefore  15.2t5 —  (sine  J°  X 
175)  =  4.58  ft.  =  the  distance  between  tangent  of  location  and  tangent 
to  a  simple  4°  curve,  which  will  occupy  the  same  position  as  the 
" central  curve"  to  within  175  ft.  of  the  points  at  which  the  simple  curve 
joins  the  parallel  tangent. 

Case  II.  applies  to  the  infrequent  contingency  when  the  exact  point 
of  curve  and  point  of  tangent  are  of  paramount  importance. 

Case  III.  is  mainly  of  use  in  the  adaptation  of  transition  curves  to 
the  ends  of  simple  curves  already  built  and  in  operation. 

Tables  XII.  to  XVIII.  inclusive  give  data  which  will  show  the  changes 
in  line  which  will  follow  the  use  of  the  various  transitions  given  in  Tables 
I.  to  X.  inclusive,  when  only  a  part  of  the  original  curve  is  changed. 
These  tables  evidently  will  apply  only  to  long  curves,  as  it  is  not  advisa- 


CURVE    EASEMENTS.  141 

fole  to  introduce  an  u  intermediate  curve"  (joining  easement  and  located 
curve)  which  shall  differ  much  in  degree  of  curvature  from  the  located 
curve. 

The  various  modifications  of  the  first  problem  of  Case  III.  will,  how- 
ever, generally  give  data  for  eased  curves  which  will  relieve  that  difficulty 
somewhat  and  will  not  require  material  changes  in  the  roadbed  if  judi- 
ciously applied. 

It  is  important  to  observe  in  all  the  problems  under  Case  III.  that  if 
the  line  AB  falls  inside  of  the  line  AM  instead  of  outside  of  that  line,  as 
shown,  that  the  angle  BAM  becomes  a  negative  quantity  and  is  to  be 
used  as  such  in  the  formulas. 

Case  I V .  is  difficult  to  apply  only  because  the  point  E  is  hard  to  find 
in  an  old  curve  when  a  transition  between  the  brandies  has  been  attempted 
by  trackmen.  It  can  be  found  near  enough  to  its  original  position  by 
establishing  D  on  the  lighter  branch  and  B  on  the  sharper  branch  at  suf- 
ficient distances  from  the  supposed  location  of  E  and  using  the  degree  of 
curvature  of  either  branch  to  determine  the  exact  degree  of  curvature  of 


I  UNIVERSITY  ) 


142  CURVE   EASEMENTS. 

the  other  branch  and  the  position  of  E,  by  the  well  known  formula  which 
determines  the  radius  and  extent  of  one  branch  of  a  compound  curve, 
when  the  radius  of  the  other  branch  and  the  controlling  angles  and  dis- 
tances are  given. 

The  use  of  Case  IV.  is,  in  many  instances,  as  valuable  as  those 
which  precede  it,  for  the  same  purposes  of  turning  trucks  gradually  and 
elevating  outer  rail  consistently  with  degree  of  curvature. 


11 


I: 


Pro/oncfaft 
"C  'of  Takers. 


Uj    3 
^> 

SI 

« 


.:•* 


V     £ 


/?g 

. 


«4 

i 


N 


149V. 

fe 

*|B 

*x& 

|-i!> 

!i* 
&?? 

4il 
&% 


m 

*  *£ 

§§i 

^Cvl^ 

Jo^' 

kjQ 
<M 

I 


CASE  I;     Ca/Ci//atf'on  /Jv  fan  gent  fencffff'T  "of  a  given  centra/  curve 
crncf  ecrsemenf  s/tnt/ar  erf  earcfi 


Use  any  st//fo6/e    easement  dHC  .' 


/cc 


Me* 


.  c. 

.  o. 

of  cenrrct/  curve  , 


.    . 
JA/*  T* 


K. 


f/re/r 


°  /5\  #=  //46  <9  , 

of  c  war  fare  every  2S&  <See  7AffL£  J2C. 


-  //2.73 


XC  •        7  SO 


COS  //*  7/2 


=  338  27 


Cor/cutation  for  ce/?fra/  Curve 
easeaf  sin?/ /arty  art  ecfC/7    enaf . 

length  "T'  erne/  /nfersectior?  crngte  I given .. 
iSo/vf  f/rst  for  jirnp/e  curve  >yitnj  orncf  7" 

of  simp fe  ct/roe  *  /  Jffffions   of  /0Oft. 

easement  JtfC,  its  /engtn s /'jfations  of/OOfff  its  curvafure  =  o(.  degrees       ^ 
:  -£l-  <* .  ~  <x'  _  appro*.  a"egree  of  centra/  curve( 


/.  /?  =  A^^LZ^-  AT  (5) 

/f  transition   £/ir  not  su/'faA/e,  assume  otner  easements 
trans/  •/  '/on  fo  OL'  /$  saf/sfacfory  antf  //no"  exact  /?  6y(3) 


/S\    7=  338.27 
333 
ecrse/ne^f  from  7br6/eJX  ford  chorc/s 


ecrsemenf 


ed  farf/?er. 
7&6/e7X  for  &  c/tora"s 


f/?e  prope 


of  /a-st 


Ca/cu/crfion   for  Easement  of  a  s/tnpfe   Curve 
a/reac/y  Autff  or  located. 

£ "   _* =^ &— 


crnef 


Chor*  JG- 


f~G  given  tn  TaA/es  marked  B. 


cr- 

r?  of  intern*.  Curve  - 


s/n-t  (CM /I + BAM + F0G) 


•  3'  curve . 


CMH    -   Tangent 

/Jrf/    =  sim/o/e.  Ctsrt/e.  Ctf  -34-2  48  A  sin.7*  . 

rfGrf  =»  cnanyc  for  easema  CM  -<  34S-&8  x  cos.7*~  339.93 

Easement-  from  7cHb/eJ2T  /'*£'  Ctort/s. 
TarAe  any  /ootnfrf  on  curve,  teyoncf  tvhicfj  it 
/S  nof  c/e s/re a&fa  to  change  //ne  offracA.  TtrAe 
a/so  a/ry point  Af  on  Tartaent  orTarroent  pro/ongecf 

O&serue  o*#/e  CAfJ  cr*a'a#yfe  BAM  between      f  ***  -_  93. 99 +3+3.  +f.  33333*  /03  S/ 
fertTfenfof/lan0'//r)etf/rf.  Measttre  rfM.         ^f 


153X 


CASE 


//?  prow'dr'ng  for  the  easement  of 
the  ends  of  a  shorf  curve  *v/>en 
the  '/nter/ned/ate  curve"  wou/d  6e 
inconren/6nf/y  sbar/y  oy  /b/ 
f>recf's6/y  the  /nefhoc/  f/' 
utafer  CdSE/ff,  an  ac/rcrnfage  mcty 
6e  Stcrcf  6y  /nor/'ng  oi/f  ffre  /rj/'c/d/e 
of  the  curve  any  desired  crmounf 
H/1. 

Put  tangent  £MB  '  para  Me  f  tv/'f/f 
tangent  at  ff,  assume  any  po/'nts 
M  and  M'  on  or/'ama/  tangents, 


ana/&s  C'MX  A-  BMM'.  Measure 
4M  artddW.  and  find  "t'nterme. 
df'ate  curyes*(nrt/ch  tv///  6e  tangrertf 
to  eacn  oMer  a?  A)  and  //'m/'ts  of 

crs  /'/?  f/rst  giren  sne 
vnder 


CASE  ///(continued). 


'/n  prdvia'/r/gr  for  fhe  easement  of  Me 
of  a  fory  curve,  when  Me  */'rtferf 

cur  ye  lYOu/a1  oe  /ncor>rer>terrft     £  \- 

7rsf  giren  under  CJSE  ///,  ar)          \ 

may  6e  S?ac/  6y  / 
ouf  fne  rrfia'a'/e  of  Me  curre 
c/es/'rec/ 


or  re  faken  erf  evert  ^farf/ons  from  JJ 

s/mjo/e    curye  dA/4  '  /S 
crnct  /1'8'  or  re  farrtgrerrts  fo 


crre  ort  or/'grrrtcr/ 

artg/es  C  M4 
''          ''' 


measure 


ftsryes  *  arro/  //m/'fe  of  casernes?  fa 
crs   /rt  mefrroc/  f'rsf  ff/'ven  tsr>c/er 


M*M'/narj/  6e  assumed  arty 


CASE  IV.     £crsement  of  trans/' f/on  from  one  Curve  fo 
"          cr  lesser  one  t'/?  the  scrme  of /reef /'or? . 


155^ 


G/utn  BFDi  £D*  6ranc/?  of  (e aser  curvature.  Choo -se  easement &Td  of  '/   """^^ 

foto/  curvature  C  </ogrt?*$  f'n  (stations  of  WO  ft.  >'/ 

let  c"^  degree    of  curve  BE^c*  cfegree     of  curve  £0  '/        __  £ ..._ 

-  GE  *  /" stat/'ons  of /OOff-t  3 f  *  f  stations  of /00ft.  A  L%^"^f^T -!^"-  !!^ 

•  B7J4  6e  S&nyent  at  ff.  and  any  fa  c~~  ornate  c  . 

'7'+  c  7' s  c  ,  ana"  /'-/-/        ^C/?orcf  dB  requires  c 

frfi-semenf  .C  fo  reared  /\^  ^          __  c 

f'ess  through  /".  ^ 

/^//  comp ounof  curve  6efw  /lana/D.  /jpprox.racftf  founcf  tnus:      y  * 

"  (fr0~*    7V.o/,r<-  J~  Mff\  // 


=    g:<T/.     (6J 
'" 


ngr  C  ,  4 
any  po/nt  D  on  curve  £D  etna/  n?ake 


,  - 

Jf  M/s  g/ve§  foo  grecft  cf/ff  oeftv  f?*R'  assume  D  further  front  F. 


6° curve  ,  £f~O  =  £°9  Easement  from  TJBLEM/6s<sume  fD=3O0'.  fhtn  «  =  6 "         ***^< 


^ 


2^. 


. 
(4):  rff=  7Ss/n2'/f'.  7$sfn  S°/J"» 


t'ng  C   t'nto  account  the  exact  rarc/tr  are 


V156 


(feyj 


^ 


? 


>*  : 

s.  N 


s? 


<*; 

K 


I! 


157 


TABLE  II. -       /OO  /? 


<3O '  Yarr/'crf/oft  , 


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9* 


JS. 


6' 


30'. 


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5° 


rjo: 


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3' 


5  8 


TA  BLC  JI  (cor>f,*uej)     /OO  ff  Cbor&s  .     3O' Vcrr/'crf/'on   . 


B.                                  Offsets     'fro* 

7    Tcrrtgfertf  fo  £"f?cfe    of  C/?oraf&  . 

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OF  THB 

UNIVERSITY 


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***c/  of  c  £/* 


fengf/r 


3*30' 


s° 


6'. 


£OO.  /O 


SSO.28 


JOO.64  JS/Je 


6'7.  72 


166 


TAB  LEV.-       3O  Ft  Chords       /S '  Var/afio» . 


A. 


O'tf    0°30 


a 


2'*$ 


3' 


J'J*' 


3  '20 


•43' 


/"/£/* 


/'/S' 


m 


^22 


*'&* 


/'to: 


'SS/t 


J'S'A' 


42L 


.MI 


£2- 


S'46/t 


a  "32 


12"  /S 


"£*& 


IL_ 


/°36' 


*{£, 


J'  J/s 


£L- 


/'£#% 


O'/S' 


2' 


3' 


TABLE!  V  (con*;****).-  SO 


>67 


B. 


Offsets   from 


fo 


of 


S°/S 


/** 


JL 


8  60 


^097 


2S06 


.  GS 


3537 


O' 


yo± 


/no 


-13- 


£L 


z  a* 


e  °£ 


4.20 


J7 


34  3 


6.67 


/S  Of 


2093 


£M. 


wo 


41 


J.7/ 


6.00 


646 


/08S 


/SS* 


S'/S 


/•S6 


322 


7  Off 


3*3 


2° 


'4$  9< 


jLJA. 


£.73 


7  66 


29£  93 


4  36 


4.96 


4*  86 


S3  9  86 


94 


99  99 


"so" 


/.  75 


S.Sf 


3.00 


>S.ffc 


S.64 


4+9.$*  399  SQ 


54964299 


4980 


/49.S4 


9998 


SO 


.4? 


4.99  S$\449. 29  393  J  7 


549.48 


S99.6> 


496.87  44698  339  /J  [3 
548  27  498  4?  448 


&LML 


&L. 


J4-9.90 


7S 


^L 


O'JC' 


Oe/3    O'30 


/'/s    rjo 


a- 


3° 


c. 


^reject/  01    of  /orrg    C/?0rafj    on   Tangent.* 
rj    of  ftaaffuS  ?c  T 


3° 


.OS 


.27 


76 


3.00 


7  6S 


/S.6/ 


Z/./3 


'168 


TABLE  V  (continue*).  _ 


Cfior&s.      /S'  Vcrrt'attor?  . 


D. 


Chorc/3. 


2*6 


2" 


/'JO' 


so. 


99.99  /49.9B 


S49.68 


299.  8/ 


399.63 


449.  S3 


S992S 


7/e 


SO. 


/49.9S 


£49.90 


299.BS 


24£2£ 


44964  499  S7 


S49  SO 


O'JO 


S39  96 


\499  69 


£°- 


/+S.99 


/99  37 


B4994 


^99. 


349-68 


44-9.82 


r/ 


so. 


37% 


/OO. 


£99.94 


349  92 


99.89 


2' 


/"JO' 


8*9  97  299.36 


349.94 


<2'J7% 


&L 


>00_ 


W,99 


244.M 


3'so' 


3'7/t 


& 


JSO 


/99.99 


£49.99 


/•/s 


4'7/a. 


S'/ 


S'37A 


£L 


/OO^. 


O'3O 


'as' 


S'7'/t 


S_'J7A. 
7*  7/i 


O'/ 


0°/S' 


r 


'  e'45'   3 


Currafure  »  c/tse  to 


or*  each  end  of  Curve  . 


of 


<y°j0' 


2' 


2'JO'\ 


3' 


so__ 


/oo. 


3OO  '6 


3SO  33 


SO'  78  \  5S2  SO  \  6Q4. 26 


169' 


TABLE  VI. 


6' 


<3e 


/I' 


20' 


/'SO' 


&. 


/a*  38 ' 


rto- 


21/S_ 


/J'JS 


6* 


f^f*. 


S'4-S 


SO* 


/'JO 


//•o' 


JV/A 


rso' 


6-20 


A* 


S'/J 


'  7/t 


7'S 


a' 


20' 


4'37/t 


3* 


/£ 


17O 


TABLE  VI  (con  f/*uec/J.  _    2S /y  C/>ortfS .        2  °  //err/*//*?*  . 
Offsets   fro*?   7ars?gre/rf  fo  e/icfs  of 


/O" 


6° 


2S.34 


JO.  74 


3S66 


4/.JZ 


2/37 


2S7/ 


28  93 


30.  7S 


J./6 


642 


S0  2/ 


96 


/7.67 


20.46 


22.  /O 


2.72 


S44 


/3  SO 


_/S_2J_ 


^_ 


2.29 


4.J9 


6.73 


S.7/ 


A9  96 


24.93 


.SS 


349 


S.O/ 


S.33 


49 


24  99 


49 


-^& 


/.42. 


3.27 


-JJ 


98 


/.S3 


99.27 


74.63 


49.87 


24.98 


1 


SS 


20* 


3° 


6° 


39 


O/ 


74.  S/ 


49.84 


24 


6' 


20 


c. 


Pro  /offffcrf/os? 

'•"  I    <5*c   I    a* 


fo  Tarrgrenf. 


.  SS 


/.SJ 


#04. 


/O.07 


/S.67 


23.24 


33.29 


20*. 

4-6.S8 


171 


TABLEV1  (conf/'nueo/) .  _     2S  ft 


D. 


C/rorcfs. 


20° 


/# 


/&* 


6° 


-££1 


4936 


33  66 


/49.06 


22268 


24-7SO 


2O  ' 


30 


<49  97 


74-98 


99.  73 


/24.S3 


/74.02 


76 


223.S/ 


49  97 


99.80 


/4949 


/74.  32 


/99. 


25 
~ 


49  98 


76 


/74.SS 


S" 


3'  30 


7' 


93  3O 


/24  84 


79 


6' 


4°  30' 


49  99 


7497 


39.94 


7  ' 


J" 


^L 


49  99 


7*98 


39  97 


6" 


/2'JO 


6"  30' 


J'JO 


SO. 


74.99 


6° 


/S' 


/9'30 ' 


7' JO 


^ 


J^ 


•££*• 


20° 


2  7°  30 


27 


22°  30- 


2Q" 


9°  JO' 


6' 


o/tse  fo 


7~arr?gret?f 


vafr  'ngr  . 


d" 


6 


20 


i  j"(?.  o/    7v5:<?<? 


/gy  ^rf  i  />f/  J<y  I    /77.68  |  g'^J'/^l  ^3^  /Z  \  ?6S.S4 


jn 


172 


TABLE  VH      ^Srf  Ckorcts. 


3° 


6' 


/S* 


£'&/* 


J"  2' 


6'4-S 


6*4-' 


26. 


S'26/i 


33%' 


4$ 


S'M 


T30 


S6- 


/C'JO 


j:.vk: 


/•so- 


JV7' 


<*'*7- 


S'M 


£SL 


£4f_ 


/W. 


/JW 


/J'JO 


/S' 


6' 


731 


TABLE  VK 


C/torct?     /*J0't/0rScrfio/?  . 


B. 


Offsets    from 


fo  enate  of 


7W 


rffig, 


3.0Z 


6-28 


/*  6S 


23  30 


26.33 


29.66 


XT 


2.70 


S.SS 


8  37 


/6.20 


2/.80 


^s. 


2  J7 


7.67 


/3.29 


7*  99 


49  3$ 


-7W 


33  9S 


74.97 


43.33 


25. 


£L 


2  04 
>£. 


/.72, 


7.44- 


/24.  67 


S3.  6  9 


74.94 


43.96 


2S. 


— 


/.33 


3.76 


W70 


S24.74 


33.8? 


7430 


49.96 


•*£ 


/.  06 


2.4f 


w. 


7<t.  36 


/24  S7 


93.  7/ 
'24.3S 


74.0S 


49.9S 


.25 
•24-5$ 


•  TV- 


'96.63 


S73.93 


93.  S3 


74.79 


24.39 


S98./0 


'73.  37 


'48.  72 


/24. 


39.4S 


43.  9  / 


.06 


246.63 


/  4  0.2  4 


/23.  73 


33.28 


74.  6S 


4  9.  S3 


24.93. 


of 


C/r  Grate   0f? 


C. 


fo  Tari/pe/?? 


.03 


/  /S       2.46 


/7./0    24. 21     33.3S 


174. 


TABLE VIK 


TABLE   VM  2S  rt  Chorc/s.     / 


r 


6' 


7' 


9" 


/O" 


f2° 


•& 


t 


/s  i     es'A  

j£l  _lai!  _ 


/r.-#ei  - 


^Hfc 


^s: 


/'SO 


/'•4 


^ 

£&& 


/'<&' 


4C 


e-  s' 


S' 


6" 


£'//' 


JW 


•SLS.L- 


Z'JO 


e^4i 
^vy' 


/O* 


7° 


6' 


/ 


//e* 


yi76 


Tangent  fo   ends    of  Cnorc/s. 


.  j°     |   4.°  J    5°     \    6°     |    7°     |    <g°     |    ^' 
/-'ro/ecf'/onsi   of  £ot?o;  Cfrorcfe    on  Tbrngent. 
Pro/ongaf/'on  of  /farcf/'us  fi>   Tangent. 


.e 


.76 


3.07 


7.69 


TABLE VM(Conffauea) .  _  <ar  rt  C6or</<s .      /'  l/a,,-af,on 


JLor?g      Chorcts  . 


S' 


3° 


7° 


6" 


3° 


2° 


es. 


74.94 


224.0? 


£9849 


4-999 


74-93 


SS.69 


'49  70 


/Z<L 


(39.4$ 


S74-.0, 


30' 


49.39 


9&.-9I 


/49.  76 


/74.  67 


/&9.S7 


7£ 


S49.36 


74.97 


33.33 


/£4.  8Q 


/49.  as 


76 


SS. 


/49.S7 


/T4.83 


£& 


SO. 


74-96 


39.36 


/S4-.94- 


/'30 


*£• 


74.39 


S9  /S 


je± 


74-39 


£5^ 


/O'3O 


S3' 


/J* 


*S_L3_1#S_ 


¥te 


SO 


*°30 


3°  30' 


£L 


I'JC 


AS0 


/S' 30'  /0"JO 


J' 


SI 


6° 


7° 


9" 


/O' 


//* 


Curyaftsre 


/fa  cosr?/DOW?c//''?gr  erf  earcf?    es?c/  of 


Tar/Tffertf 


of 


~^ 


£L 


-so. 


&L 


/OOOS    V2S.S4     /SO  32 


76  3OB86 


178 


TABLE.  IX.-  ss  rfcs>orc/s.   w  Vartatfo* . 
A. 


J* 


J'JO 


4'  JO 


J'JO' 


6" 


JZt 


/•//% 


0'<so' 


JS 


/•  e' 


/'JO' 


soi 


3'7/t' 


/•jo- 


/•Jo> 


£6' 


** 


49' 


<*' 


2*30' 


S 


30 


/•£*! 


/•/J- 


3'* 


/•&8' 


/•S7'/z 


-*& 


s 


/•#> 


'33%' 


S'/S' 


3'33'A 


e^m 

j*/?' 


siti 


O"30' 


/'30' 


2' 


S'30 


J' 


#•30 


TABLE  IK  (conduce/). _  ss  /:/  cs?or</*.   so 


179V 


a. 


Offsets   from 


fo  e/?cfo  of.CS?orcf&, 


'    2* 


/°30     / 


& 


a.  36 


'0*3 


/7.06 


^ 


O°30 


/./K 


Z.34 


3./S 


/J.f/ 


S3.  78 


*''0 


$°^- 


&L 


S./S 


S.S6 


39.99 


74.99 


J.32 


3°  30- 


/K4  97 


-?4J99_ 


22 


JS.+6 


-W-A?. 


•9*97 


74.96 


•99.  9S 


49.99 


/.ss 


/.SO 


2*30' 


/99.7S 


99.94 


74.97 


49.99 


W.ao 


/7&.6S 


99.  OK 


74.9  ff 


&L 


49.98 


T3 


-££ 


/4S.67 


O°3O 


/?* 


3*30' 


c. 


Pro/echo*    of  to/?ff    Cfrorc/s   on  Torngrerrf 
Pro/onycrt/'os>    of  /?cre//t/s 


3°  30' 


JS 


•*£- 


/SO 


J-** 


S.sa 


OF  THB  ^^^ 

UNIVERSITY  J 

=   -VK    V 


V18O 


.  _      2S  /7 


3O  ' 


O. 


3"  30' 


2°30 


8° 


/'JO' 


0°30'. 


~0*3d 


JU 


a 


'±?-9L 


2B477 


S49J2 


2V466 


£39.62 


6" 


/49.SS 


224.62 


ZW.7S 


s° 


7^1 


A/5 


z^ 

T^XF 


J^ 


.5^ 


74.99 


/S4.97 


/T4.94 


£24.9' 


TW 


v^ 


rss/* 


/'30' 


>9$  9S 


3°  JO' 


'24.93 


ss_ 


'24.99 


3°  30' 


°  30' 


^f.L 


4^ 


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/94-.9S 


4^5?; 

^V<7 


^l^e/s  4'ftx 
**r/t 


7"  JO" 


J' 


&* 


23... 


7S\. 


So. 


ft? 


/C30' 


2*30       3" 


3°30' 


6°. 


Gt/rvafare    a/v«  fo   com/Dotsrra/tnff    erf  earcfi  en  of  of  Curve, 
of  com/oounc/'ty  . 


2*30' 


3°3O' 


6° 


SS 


60. 


7S. 


/oo.ot 


/2S.03 


/SO  04 


/7S.  /6 


SOO.  31 


SZS.S4 


ZS0.83 


£76.40 


JOS./4. 


isi1 


..        25  &  Chora's. 


'-Variation. 


A. 


a* 


£22 


3'tf' 


0°/S 


/'/*' 


/"4S- 


2°  6'A. 


2°33' 


£'  /?' 


!» 


36% 


S3 


SO  tit 


£"/?' 


/"JO' 


89* 


29' 


39'A 


36% 


.*<ai 


34 


-if 


44-' 


# 


^26' 


/w 


3* 


82 


TABLE  X   (conn  »***}.  — 


y  CS)Orc/s.      /S  ' 


Offsets  from 


/o  es?ofc  of  C/foraf-S  . 


/'JO' 


O"/S' 


0'  ' 


3  69 


SO 


4.SS 


S.40 


^L?7 

609 


..8.S+. 
6~.6/ 


_  8.86 


-sJ."— 
2*45 


/  OS 


Z4S 


3  BO 


499 


S.2S 


75 


SO 


.40 


/  28 


77 


2.  22 


278 


2' 


/IS. 


/OO. 


SO. 


25 


22- 


34 


.68 


/06 


/  9/ 


'2+99 


'00 


75. 


£3- 


.£9 


es 


'24-  99     99  99 


2- 


/9997 


97 


7S. 


so_ 


25 


£S_ 


22494 


/  74.96 


74.99 


SS_ 


_££. 


O'<4S 


249. 9 V  2Z4.9/. 


49.9S 


S9.36 


74-99 


•JZL 


O"3O' 


2-4S 


£74-  as  249  86 


224.87 


/99  89 


'24.96 


99.38 


74 99 


SO- 
74.99 


SJL. 


£L 


299  78  \274  7# 


249.90  \3S4  83 


86  /74 


0"/S' 


2  'JO' 


3' 


c. 


of  /o 


of 


C/rorofs    on  Tctr>grent. 
s  fo  Tangent, 


O°3O' 
.07 


/ff 


73 


/'JO' 


2.78 


3  69 


2  "JO 
S.26 


8  <39 


TABLE  3T.  (confini/ecf) 25  f~S  Cfor&s  .       /J' '  Vcrr/crf/on 


D. 


Cfiorafs. 


2° 


'  rw  /vj'  /• 


'   0'30'  Q'/S 


<4££<L  /7*SL  J3&±S\A&L3j*  2.49.93 


299  S  V 


J* 


S3 


33.36 


S24.96  243.3S 


274.34 


J/U 


rt* 


£L. 


SO. 


&. 


js_ 


33  S3 


'24.99 


24336 


SO, 


f43.99 


/74.9S 


/393S 


2B497 


37S* 


SJ^ 


/4S.99 


'7*.  & 


8' 


'££, 


/74.S3 


£L 


sa_ 


'00 


/SO. 


/'7& 


so_ 


/2S. 


2S^ 


SO. 


7S. 


/OC. 


zs 


<?v 


Mi 


SO. 


7S. 


/'//& 


&L. 


ZA. 


sw 


~r 


•4'  30' 


Z'SW 


O'/S 


8° 


'    2*30' 


Curfcrftsre    afve  fo 


erf  fcrch  eicf  of  curve. 


of 


0°30 


2"/S' 


£'30' 


3* 


SO 


7S 


/OO 


/so  os 


/7S.04 


SOO  Off 


2SO.SS 


27S.3S 


3OO.S 


-/T84 


^ 

5! 
5 


D  «  no.  feef  of  &'m/o/e  Cur  re  cftangec/. 
C's  Degree  of  f'nfermeaf/'crfe  Curre, 
L  «  Distance  /'»  Feef  from  PC.  of&mpJe  Curve 
to  PC.  of  Easement* 


eef  Sefw 
Curve  . 


n 


Max  /mum  Of 
ort'gffna/  and 


1  85 


Feet  of 


of  /nferme 
in  Feet  fr 
Easement. 
m  Offset 
<yf?cf  eas 


Degr 
Dista 
to  PC. 
ofx 


.  of 
O  *  Mofx/frr 
orig/'/ja/ 


*S 

* 

I 


X 


§* 


X     S  -K 

H* 


I? 


<$    'b 

^ 


S 


S«i 


\? 


«  * !  5|> 
Nl^l 


187V, 


iw 


s 


.ll 


n     ii    ii 


^  ^  |  -| 


I 


* 

5 


Tl 


<'  J? 

I 

^ 


189V 


. 


UNIVERSE: 

CALIFOR^L 


191V 


! 


i*i 


u 


•5  S 


II 


' 


1  ADVERTISEMENT. 

fi 


THE   APPLICATION^^  SERVIS     TIE     PLATES 
TO  SWITCH  LAY-OUTS 


Having,  in  the  previous  chapters,  diagrams  and  tables,  piven  de- 
tailed instructions  for  the  accurate  laying  out  acd  proper  putting  in  of 
switches,  we  herein  present  a  few  hints  as  to  how,  under  the  heaviest 
traffic,  with  little  expense  for  labor,  the  good  work  can  be  made  to  stand. 
For  it  is  to  ihe  permanency  of  the  work  that  the  considerations  of  safety, 
efficiency  and  economy  relate. 

In  our  switching  yards,  the  labor  of  track  repairs  is  very  costly.  Tbe 
frequency  of  trains  results  in  constant  interruption  to  the  trackmen,  and 
thorough  work  can  only  be  done  at  the  expense  of  delay  to  traffic,  which 
is  not  permitted.  For  the  protection  of  trainmen,  the  ballast  filling  in 


ADVERTISEMENT. 

yards  is  kept  full  up,  thus  impairing  the  surface  drainage  of  same,  which 
tends  to  keep  the  ties  soft  and  more  liable  to  cut,  while  the  deficient 
drainage  leads  to  the  churning  of  the  ties,  which  is  aggravated  by  the 
cutting  of  rails.  The  labor  of  changing  switch  sets  in  our  busy  yards,  by 
accurate  records  kept,  costs  from  80c.  to  more  than  $1.50  per  tie. 

The  conditions  above  stated  all  tend  to  that  general  looseness  of 
parts  which  characterizes  the  tracks  of  many  of  our  leading  yards  and 
makes  constant  tinkering  necessary  to  preserve  safe,  when  reasonably 
good  track  at  less  cost  for  labor  could  be  obtained. 

Where  physical  conditions  are  unfavorable  and  work  on  track  is  sub- 
ject to  constant  interference  of  traffic,  as  in  yards,  the  application  of  de- 
vices which  supplement  and  afford  a  substitute  for  labor  add  greatly  to 
the  efficiency  and  economy  of  maintenance.  It  is  this  experience  which 
has  led  many  lines  to  adopt  the  Servis  Tie  Plates  for  the  protection  of  ties 
in  switch  lay-outs  and  switching  tracks,  and  thereby  better  track  has  been 
attained  at  greatly  reduced  cost  for  both  labor  and  material.  Switch  sets, 
which  formerly  cut  out  in  eighteen  months  and  two  years,  have  been  pro- 


3  ADVERTISEMENT. 

tected  with  plates  for  more  than  three  years  and  give  promise  of  con- 
tinued service  until  decay. 

The  plates  render  the  use  of  rail  braces  unnecessary  ;  they  hold  the 
track  to  gauge  a  ad  the  rail  does  not  cant  or  cut  into  the  tie,  while,  by 
preventing  the  cutting-in  of  the  tie,  the  pumping  action  of  the  rail  is 
arrested  and  the  churning  of  ties  is  minimized.  These  considerations  will 
at  once  suggest  the  saving  of  labor  resulting  from  their  use,  viz. :  less  fre- 
quent changing  of  ties,  no  adzing  of  ties  or  rolling  up  of  rails,  while  re- 
gauging  of  the  track  is  avoided. 

In  busy  yards  the  life  of  ties  and  switch  and  frog  sets  can  be  pro- 
longed to  their  natural  lives,  as  the  ties  are  protected  from  the  cutting 
action  of  the  rail  and  frequent  spiking  for  regauging  is  avoided.  The 
life  of  rails  is  preserved  by  holding  them  perpendicular  to  the  plane  of 
the  tie,  by  which  means  the  excessive  side  head  wear  is  prevented  In 
addition  to  this,  a  general  saving  in  labor  and  material  is  secured  by  the 
perfected  fastening  wnich  the  plate  affords,  thereby  correcting  the  gen- 
eral looseness  of  parts,  so  destructive  to  track. 


ADVERTISEMENT. 


Plates  should  be  driven  home  when  applied,  and  a  tool  for  this  work 
is  furnished  at  cost. 

Upon  application  to  the  Q.  &  C.  Company,  of  Chicago  and  New  York, 


who  are  the  manufacturers,  references  will  be  given  covering  any  applica- 
tion desired,  viz.:  to  switch  and  frog  sets,  yard  curves,  under  planking  of 
street  crossings,  station  platforms,  etc.,  and  for  general  yard  purposes. 


ADVERTISEMENTS. 


MCGONWAY  &  TBRIIEY  GQ. 

PITTSBURGH,  PA. 


MANUFACTURERS   OF 


RAILROAD  MALLEABLE  CASTINGS 

RAIL     BRACES 

FROG  PLATES  WRENCHES 


ADVERTISEMENTS. 


Hydraulic 


KAIL  BENDER. 


Headquarters  for 

of  .  .  . 
.  .  .  Jlydraulie  Jools 


Jacks 


WEB  PUNCH. 


SEND  FOR 
CATALOGUE  VIII. 

The  WATSON  &  STILLMAN  CO.,  204-210  East  43d  St.,  New  York. 


WRECKING  JACK. 


ADVERTISEMENT^. 


ELLIOT  FROG  &  SWITCH  CO., 

EAST  ST.  LOUIS,  ILLS. 

EUREKA"    SPRING    RAIL    FROG 


EUREKA"     SPRING     RAIL     FROG 


STEEL    CLAMP    FROG 


HIGH    MAIN   LINE 
STAND 


ADVERTISEMENTS. 


8 


WEIR    FROG    CO., 

CINCINNATI,  0. 

We  illustrate  here  the  simplest  arrangement 
of  a  Three-Throw  Split  Switch  on  the  market. 
Full  strength  of  switch  rails,  no  weakening  by 
slotting  for  Switch  Rods.  Adjustable  Connecting 
Rods  provide  easy  and  positive  adjustment  of 
Switch  rails. 

The  only  arrangement  of  this  device  operated 
by  a  Single  Low-Target  Ground-Throw  Stand. 

Adjustable  Split  Switch 
Improved  Spring  Frogs. 
Bolted  and  Clamped 

Rigid  Frogs. 
Automatic  "Clutch- 
less"  Spring  Switch 

Stands. 
Steel  Die  Formed 

Rail  Braces. 


WEIR  FROC  CO.'S  THREE-THROW  SPLIT  SWITCH  WITH  UOW  STAND 


ADVERTISEMENTS. 


,    Biting    £    Co., 

LIMITED, 
Pittsburg,    Pa. 

TRAGK  •  SHOVELS. 


JOSEPH  F.  McCOY  CO. 

din  GROW  RAIL  BENDER 

WROUGHT  JRON  AND  STEEL 

Five  Sizes  in  Stock  for  20  to  90  Ib.  Steel  Rails. 

.  .  .    ALbO    .  .  . 

HYDRAULIC  RAIL  BENDERS 
TRACK  GUAGES  AND   TRACK  LEVELS. 

TRACK  JACKS  AND  DRILLS 

26  WARREN  STREET          -        NEW  YORK. 


ADVERTISEMENTS. 


10 


THE    TRUSS    RKIL     JOINT 


References  by 

Permission : 
C.  &N.W.RY. 
C.M.  &ST.  P.RY. 
C.  ST.  P.  M.  &  0.  RY. 
F.  &  P.  M.  RY. 


IT    COMBINES    STRENGTH    AND    FLEXIBILITY. 

gEVEN  YEARS  practical  test  of  5  Miles  of  these  Joints  proves  that  it 
adds  25  per  cent,  to  the  LIFE  of  the  Rails,  and  reduces  cost  of  mainten- 
ance of  Joints  40  per  cent. 

THE   TRUSS    RMIL.  JOINT  OO., 

H.  H.  McDUFFEE,  General  Sales  Agent.  1118  Marquette  Building,  Chicago,  1IL 

Orders,  1896:    3^  miles -30,000  joints.    C.  &  N  WM  36  miles ;  Mich.  Cent.,  27^  miles; 

C.&Bluelsd,  20  miles. 


11 


ADVERTISEMENTS. 


Beff  filer  TEIJoit,™  if  6toSt8i  Join 


Permanently  maintains  surface  and  alignment,  embodies  all  the  advantages  of  a  tie  plate  and  nut 
lock  with  perfect  spiking  opportunities,  and,  since  no  part  of  the  joint  is  below  the  tie  surface,  makes 
it  pos-ible  to  lay  either  supported  or  suspended. 

The  wood  filler  is  incrersed  in  the  channel  and  shoe  argle,  and  being  made  a  trifle  too  large  is 
squeezed  into  position,  keeping  all  the  parts  tight  and  reducing  the  noise  to  a  minimum. 

THE  WEBER  RAIL! AY  JOINT  MANUFACTURING  COMPANY, 

Principal  Office:  Cotton  Exchange  Building,  Hanover  Square,  NEW  YORK  CITY. 
Branch  Offices:  Ho.  70  K,lby  St.,  BOS  TOM,  MASS.,  and  1790  Old  Colony  Bldg.,  CHICAGO.  ILL 


ADVERTISEMENTS. 


IRON    CITY    TOOL    WORKS,    Limited 
^tapdard  Railroad  Jrael( 


Best  Quality 
Best  Work 

Best  Result 
IN  TRACK  TOOLS 


Strongest  Spring  Ever  Nade 

CANT  be  equaled 
CAN'T  injure  bolt  or  nut 
CAN'T  be  put  on  wrong 


[EUREKA  F>at.DeceLM887 


Try  EUREKA  on  Track  Joints,  Bridges,  Frogs  and  Crossings 
EUREKA    NUT    LOCK    COMPANY 


SAMPLES  FURNISHED  ON  APPLICATION. 


Pittsburgh,  Pa. 


13 


ADVERTISEMENTS. 


THE  QREER  R.  R.  SPIKE  CO. 


The  Qreer  Spike  is  the 
only  Spike  with  a  Keen 
Ground  Point,  Separate 
Driving  Head,  Adequate 
Holding  Power.  Hand 
Packed.  Made  by  the 
Cheapest  Process  yet  dis- 
covered, therefore  Sold  at 
Bottom  Market  Prices, 
with  guarantee  of  100  per 
cent  perfect  spikes. 


CHICHCCX 


SAMSON  SPLICE  BAR. 

Makers  of  all  the  Samson  Splice  Bars  in 
use.     Our   Track    Fastenings    are  now 
in    use   on    408    Railroads ;    equal 
to  25    per  cent    of  the  raiJ- 
roads     of   the    United 
States.     Over  12,- 
000,000     in 
service 


The  Atlas  Rail 
Brace.    The  Strongest 
and  Cheapest  Rail  Brace  Made. 


ADVERTISEMENTS. 


14 


RICHARD  DUDGEON'S^  Latest  Improved 
l§     Jtydrauliejael^s,  pupcfyes  9 


CHEAPEST 

BECAUSE 

THE    BEST 


JUDGE  COXE,  in  af- 
firming and  fully  sus- 
taining the  validity  of 
the  Dudgeon  Im- 
proved Hydraulic  Pat- 
ent  Jack,  says,  among 
other  things : 

"  The  advantages  over 
the  1873  patent  may  be 
summarized  as  follows  .* 
More  perfect  action,  in- 
creased durability,  and 
greater  ease  in  repair- 
ing." 


presses 


RICHARD  DUDGEON, 


24  Columbia  Street,  New  York, 


15  ADVERTISEMENTS. 


THE   RAILROAD  GAZETTE 

32  Park  Place,  New  York 

Is  published  every  Friday.     It  is  elaborately  illustrated,  and  contains  more  practically  useful  information  on  Track, 
and  all  departments  of  railroading,  than  any  other  publication  in  the  World.    $4.20  a  year.     Specimen  copy  free. 

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CATECHISM  OF  THE  LOCOMOTIVE.     By  M.  N.  FORNEY.    The  most  complete  treatise  on  the  locomotive. 

Price,  $3.50. 
ELEMENTS    OF    RAILROADING.      By  CHARLES  PAINE.     A  general,  practical  description  of  the  working  of 

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CAR    BUILDERS'    DICTIONARY.      Contains  5,683  engravings  of  all  kinds  of  cars  and  details  of  construction. 

Price,  $5.00. 

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